A quadratic function f(x)=x2+8x.
a.) Find the quadratic function in standard form.
f(x)=x2+8xf(x)=(x2+8x+16)−(1)(16)Complete the square: add (82)2=16 inside parentheses, subtract (1)(16) outsidef(x)=(x+4)2−16Factor and simplify
The standard form is f(x)=(x+4)2−16.
b.) Find its vertex and its x and y-intercepts.
Using the formula of standard form of a Quadratic function,
f(x)=a(x−h)2+k
We know that the vertex is at (h,k), so the vertex of f(x)=(x+4)2−16 is at (−4,−16).
Solving for x-interceptsSolving for y-interceptWe set f(x)=0,thenWe set x=0, then0=(x+4)2−16Add 16y=(0+4)2−16Substitute x=016=(x+4)2Take the square rooty=16−16Simplify±4=x+4Subtract 4y=0x=±4−4Simplifyx=0 and x=−8
c.) Draw its graph.
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